SPI-77 and paclitaxel can be safely administered as a drug combination in patients with non-small cell lung cancer previously treated with chemotherapy. A maximally tolerated dose can be established which will characterize the toxicities of SPI-77 plus paclitaxel in patients with advanced non-small cell lung cancer, and determine the maximum tolerated dose of SPI-77 when given in combination with a fixed dose of paclitaxel administered every 3 weeks. Determine also the pharmacokinetics of SPI-77 and paclitaxel at the MTD, and assess any responses that may result from the combination treatment of SPI-77 and paclitaxel.